I am an Associate Professor in the Department of Mathematics of the University of Ioannina. I am part of the Applied Mathematics and Engineering Research Section and I am located at 313ε in the Mathematics building. My research focuses on physical applied mathematics and in particular on nonlinear waves and integrable systems.
We study a generic model governing optical beam propagation in media featuring a nonlocal nonlinear response, namely a two-dimensional defocusing nonlocal nonlinear Schrödinger (NLS) model. Using a framework of multiscale expansions, the NLS model is reduced first to a bidirectional model, namely a Boussinesq or a Benney-Luke-type equation, and then to the unidirectional Kadomtsev-Petviashvili (KP) equation – both in Cartesian and cylindrical geometry. All the above models arise in the description of shallow water waves, and their solutions are used for the construction of relevant soliton solutions of the nonlocal NLS. Thus, the connection between water wave and nonlinear optics models suggests that patterns of water may indeed exist in light. We show that the NLS model supports intricate patterns that emerge from interactions between soliton stripes, as well as lump and ring solitons, similarly to the situation occurring in shallow water.
Part of the book: Nonlinear Optics
The fundamental lattice solitons are explored in a nonlocal nonlinear medium with self-focusing and self-defocusing quintic nonlinearity. The band-gap boundaries, soliton profiles, and stability domains of fundamental solitons are investigated comprehensively by the linear stability spectra and nonlinear evolution of the solitons. It is demonstrated that fundamental lattice solitons can stay stable for a wide range of parameters with the weak self-focusing and self-defocusing quintic nonlinearity, while strong self-focusing and self-defocusing quintic nonlinearities are shortened the propagation distance of evolved solitons. Furthermore, it is observed that when the instability emerges from strong quintic nonlinearity, increasing anisotropy of the medium and modification of lattice depth can be considered as a collapse arrest mechanism.
Part of the book: The Nonlinear Schrödinger Equation